Arvind Pai Thesis

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Stocks Are From Mars, Real Estate Is From Venus:An Inquiry into the Determinants of Long-Run Investment Performance

By

Arvind Pai

Diploma in Architecture, 2000

TVB School of Habitat Studies

Submitted to the Department of Urban Studies and Planningin Partial Fulfillment of the Requirements for the

Degree of Master of Science in Real Estate Development

at the

Massachusetts Institute of Technology

September, 2006

2005 Arvind PaiAll rights reserved

The author hereby grants to MIT permission to reproduce and to distribute publicly paper andelectronic copies of this thesis document in whole or in part in any medium now known or hereafter created.

Signature of Author______________________________________________________ Arvind PaiDepartment of Urban Studies and PlanningJuly 28 th, 2006

Certified by______________________________________________________________ David M. Geltner Professor of Real Estate Finance, Department of Urban Studies and Planning

Thesis Supervisor Accepted by_____________________________________________________________

David M. Geltner Chairman, Interdepartmental Degree Program inReal Estate Development


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Stocks Are From Mars, Real Estate Is From Venus:An Inquiry into the Determinants of Long-Run Investment Performance

By

Arvind Pai

Submitted to the Department of Urban Studies and Planningon July 28 th , 2006 in Partial Fulfillment of the

Requirements for the Degree of Master of Science inReal Estate Development

Abstract

This thesis presents an inquiry into the historical performance of core institutional real estate investment

property during the 1984-2003 period. The focus of the analysis is on identifying systematic determinantsof long run investment performance. The analysis seeks to increase our understanding of equilibriumasset pricing within this asset class, as well to provide some useful perspective for core portfolio strategicor tactical planning. This thesis extends earlier research by Geltner (1999) and Li and Price (2005) thatindicated that a classical single-factor CAPM accurately modeled the cross-section of long-run totalreturns across the major asset classes, including real estate. The present thesis narrows that earlier focus toconcentrate on the cross-section of long-run total return performance within the core institutional realestate asset class. This thesis uses the property level data of the NCREIF Index to construct portfolios andhistorical return indexes based on property size (value), and based on CBSA tier (that is, upper,middle, and tertiary cities from an institutional investment perspective).

By using unique portfolios created from the NCREIF property set that represent possible factors that

systematically affect asset pricing, such as property location, property size and property type, andcalculating their beta estimates from historical data, this thesis tests various CAPM models including thesingle factor Sharpe-Linter model, as well as a multi factor Fama-French-like model. The beta for the

portfolios was defined with respect to the performance of the aggregate of all NCREIF properties.

This thesis finds that an equilibrium asset pricing model consisting of the two Fama-French-like factors, property size and MSA tier, plus property type dummy variables, explains some 90% of the long-runhistorical cross-section of core property portfolio returns. Interestingly, the market factor, the beta withrespect to aggregate NCREIF, is found to be insignificant, and possibly a negative influence on expectedreturn. Furthermore, the size factor works opposite to the way it does in the stock market, with larger

properties commanding an expected return premium. Surprisingly, the city tier factor gives an expectedreturn premium to upper tier cities. Tests for an income factor (similar to the Fama-French book-to-

market factor) found this factor to be insignificant. The most significant factor was found to be the property type. Thus, the equilibrium asset price model that seems to work well within the institutionalcore real estate asset class seems to be very different from, almost opposite to, the analogous modelwithin the stock market.

Thesis Supervisor: David M. Geltner Title: Professor of Real Estate Finance


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Table of Contents

Abstract ............................................................................................................................... 2

Table of Contents................................................................................................................ 3

Acknowledgments............................................................................................................... 4

Introduction and Background ............................................................................................. 5

Introduction................................................................................................................. 5

Literature Review........................................................................................................ 7

Methodology & Data ........................................................................................................ 13

Methodology in Brief................................................................................................ 13

Detailed Methodology Part I Data Analysis .......................................................... 14

Detailed Methodology Part II Asset Pricing Models............................................. 39

Analysis & Findings ......................................................................................................... 44

The Single Factor Capital Asset Pricing Model ....................................................... 45

Three Factor Fama & French Based Asset Pricing Model ....................................... 50

Summary & Conclusions .................................................................................................. 54

Study Limitations and Scope for Further Research .......................................................... 56

Bibliography ..................................................................................................................... 58

Appendix........................................................................................................................... 60


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Acknowledgments

I am extremely grateful to my advisor Professor David Geltner for his guidance, encouragement

and insights. Dr. Geltner has the unique ability to instill his passionate thirst for knowledge in his

students and encourage them to strive for excellence. I thank him for leading me to the cutting

edge and beyond.

I would like to thank Cate Polleys (CRE 1997) and John Barrie (CRE 1994), who provided the

seed for this study. Their guidance and perspective proved invaluable for this research.

I am grateful to NCREIF for providing me with the database for this study. Without their

contribution this study would not have been possible. I would also like to thank Jeff Fisher for his invaluable assistance and support.

Most importantly, I would like to thank my wife. Without her encouragement I would not be at

M.I.T.


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Introduction and Background

Introduction

With the recent increase in interest in the real estate asset class by investment fund managers

there has been much focus on the allocation strategy within the real estate asset class. This study

attempts to provide some guidance to real estate core fund portfolio managers by exploring the

historical performance of core 1 properties within the NCREIF index from the 1984 to 2003

period.

Previous research by Geltner (1999) and Li and Price (2005) have indicated that a classical

single-factor Capital Asset Pricing Model (CAPM) accurately modeled the cross-section of long-run total returns across the major asset classes, including real estate. It has been shown that the

basic Sharpe-Linter CAPM does work, in essence, for real estate after all, at least at a broad-

brush level across the asset classes. This is the level that is useful for mixed-assets portfolios,

that is, portfolios that potentially include all major asset classes.[Geltner and Miller (2001),

p.572].

The present thesis narrows that earlier focus to concentrate on the cross-section of long-run total

return performance within the core institutional real estate asset class. The focus of the analysis is

on identifying systematic determinants of long run investment performance. Although it has been

demonstrated [Geltner and Miller (2001), p.574] that that the basic single factor CAPM cannot

be applied within the real estate asset class, this study attempts to test a multi factor asset pricing

model over core properties within the NCREIF property set. Multi factor models have been

tested successfully by the Ling and Naranjo (1997) paper, however my study is based on a

different Fama and French like model that seems more directly applicable to the investment

decision making process of portfolio managers.

To identify the potential systematic determinants or factors that determine asset price I worked

with factors that previous research has determined to be statistically significant or that represent

1 Core is defined as properties that have regular capital expenditure and do not undergo substantial renovation or opportunistic repositioning.


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specific identifiable characteristics of core commercial real estate that the market may price, and

eliminating them if they proved insignificant.

Representing classical financial economics as proposed by the Sharpe-Linter CAPM, the market

factor was introduced as the primary factor. The property size (value) factor was also a

potential determinant as demonstrated by Ziering and McIntosh (1999). Property location as

determined by the CBSA tier(that is upper, middle and tertiary from an institutional

investment perspective) was also determined to be a significant factor by Hess and Liang (2005)

although their definition of Tier is based on CBSAs with similar economic drivers rather than

total investment value as in my study. An income factor was also introduced to address the

potential preference of investors for income return over capital return given that real estate

investments are often long term in nature and provide significant and relatively stable cash flow.

By using unique portfolios created from the NCREIF property set that represent these factors,

and calculating their beta estimates from historical data, I was able to test the various CAPM

models including the single factor Sharpe-Linter model, as well as the multi factor Fama-French-

like model. The beta for the portfolios was defined with respect to the performance of the

aggregate of all NCREIF properties rather than with respect to the National Wealth Portfolio

(NWP). This simplification avoids appraisal bias, and is consistent with classical CAPM theory

under the assumption that the national wealth-based betas of property portfolios equals their

betas with respect to NCREIF times the beta of the aggregate NCREIF portfolio with respect to

national wealth.

Interestingly, the creation of these unique portfolios also allows me to explore the herd

mentality of the NCREIF members as demonstrated by the over weighted 2 nature of the index

in a few CBSAs and certain property types and sizes. By creating portfolios based on property

type, property size (value), and based on CBSA tier (that is, upper, middle, and tertiary

2 Over weighted as reflected by the high concentration of NCREIF assets in a few CBSAs that is far in excess of the proportionate contribution of these CBSAs to the US economy in terms of income, employment and population


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from an institutional investment perspective), this study compares the historic performances of

peripheral and mainstream properties on a risk-adjusted 3 basis.

The 1984-2003 period was selected as it represented an entire real estate cycle and avoided the

recent run up in real estate prices which I consider an anomaly that could possibly skew the data.

Additionally, beginning from 1984 allowed me to have a sufficient number of properties in each

portfolio so as to adequately represent the portfolio returns. This would have not have been the

case had I started from 1978, the period that the NCREIF dataset began.

The study begins with a description of the relevant literature review that formed the basis for this

study and is followed by a section focused on both the methodology for the generation of the

unique portfolios, as well as on the methodology for the asset pricing models. The next sectionfocuses on the findings of the asset pricing models and presents the data for the most appropriate

model. This is followed by a section that summarizes and concludes the study and describes its

relevance to the decision making process for real estate core fund managers. The last section lists

the limitation of this study and suggestions for future research.

So lets begin Stock Are From Mars, Real Estate Is From Venus and in the words of a very

wise professor 4 the important thing is to enjoy yourself.

Literature Review

The starting point of this research is based on the Capital Asset Pricing Model (CAPM). [Sharpe

(1964), Lintner (1965)]. The CAPM first introduced the concept of separating risk into

systematic risk and idiosyncratic risk. Systematic risk is the risk associated with holding the

market portfolio and it is rewarded by the capital market. Idiosyncratic risk is specific to a

particular asset and can be diversified away when held in combination with other assets and,

thus, is not rewarded by the capital market. CAPM theory says that an assets contribution to

portfolio risk depends on the assets sensitivity to changes in the value of the market portfolio.

3 The measure of risk in this section of the study is the Market Beta where the Market is defined as the aggregate NCREIF investment portfolio.4 Yes, it is Prof. David Geltner


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Systematic risk, or the marginal contribution of a given asset to the risk of the market portfolio,

can be measured using beta. Beta is calculated 5 as follows:

i = cov(r i,r m) / m2

where

cov(r i,r m) is the covariance between the asset return and the market return, and

2m is the variance of the market return

After calculating beta, the remainder of the CAPM formula is:

E(r i) = r f + i[E(r m)-r f ]

where

E(r i) is the expected return of an asset

r f is the risk free rate

i

[E(r m

)-r f ] is beta times the market price of risk (or risk premium)

There are of course certain simplifying assumptions made by this model such as the absence of

secondary costs such as taxes and transaction costs. This model also assumes that all investors

have identical investment horizons, identical perceptions regarding expected returns, volatilities

and correlations.

The returns provided by the market have been compared with the results of the empirical testing

of the CAPM model. Most tests take a representative value weighted index, such as the S&P 500

as a proxy for the market portfolio, and then check whether the historical average return on a

security can be explained by the equation. These studies focus on whether beta alone can explain

5 The author would like to acknowledge that part of this literature review is based on that done by Nan Li and StevenPrice for their thesis on Multiple Asset Class Investing, MIT Center for Real Estate, August 2005.


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the historical average returns on portfolios. Although the results support the concept of a linear

relationship between expected return and beta, the simple beta calculation doesnt present the

most accurate measure of expected return. Two important early tests were by Black, Jensen and

Scholes (1972) and Fama and McBeth (1973). More recent studies include Fama and French

(1992) and Black (1993).

The most relevant CAPM based model was proposed by professors Fama and French. In their

1992 paper, they conclude that there are three factors which together do a good job of explaining

risk pricing by the capital market. The factors are a market factor, a size factor and a book-to-

market factor. The proposed CAPM based model has been described below:

E(r i) = r f + market (r market factor ) + size(r size factor ) + book-to-market (r book-to-market factor )

Where

market factor: return on market index minus risk-free interest rate

size factor: return on small-firm stocks less return on large firm stocks

book-to-market factor: return on high book-to-market-ratio stocks less return on low book-to

market-ratio stocks. [Breeley and Myers (2001), p.209]

This model has been found to be fairly accurate in describing market pricing of securities within

the stock market. This approach has been used extensively in this thesis to model real estate asset

pricing by the market.

The Geltner and Liu dissertations have found that the basic Sharpe-Lintner CAPM does work,

in essence, for real estate after all, at least at a broad-brush level across the asset classes. This is

a level that is useful for broad strategic and tactical investment policy making for managers

responsible for mixed-asset portfolios, that is, portfolios that potentially include all the major

asset classes.[Geltner and Miller (2001), p.572].


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The CAPM should conceptually work within the real estate asset class, however the Geltner

study has shown that the basic CAPM, with a single risk factor based on asset periodic returns

volatility or covariance with a single risk benchmark, does not seem to work very well. [Geltner

and Miller (2001), p.574]. As a result much of the recent asset price testing involving real estate

moved away from the standard single-factor CAPM in the direction of more robust multi-factor

modeling. The empirical advantage of multi-factor models, from a statistical perspective, (is

that) the more explanatory variables you have in the right-hand side of a regression of asset

returns onto risk factors, the more variability in asset returns you can explain with the

regression. [Geltner and Miller (2001), p.579].

The most interesting of these multi factor models has been the one proposed by Professors Ling

and Naranjo (1990). Their study moved beyond the scope of the previous studies that simplylooked at publicly traded real estate and actually applied arbitrage pricing theory (APT)

modeling to private real estate. They noted that many studies have focused on the linkages

between stock and bond market returns and macroeconomic events such as fluctuations in

interest rates, inflation rates and industrial production. They suggest that due to the comovements

of real estate and other asset prices these same systematic risk factors were most probably priced

in real estate markets. Their findings are described in two articles, Ling and Naranjo (1997) and

Ling and Naranjo (1998).

Their study identified the changes in real estate per capita consumption, the

real T-bill rate, the term structure of interest rates, and unexpected inflation as fundamental

drivers or "state variables" that systematically affect real estate returns. They also introduced

conditioning variables that are not risk factors per se but are prior characteristics of the assets

that help to predict ex-post returns. Factors used in my model are property specific as opposed to

the macro economic risk factors used by Ling and Naranjo.

There have been several studies that explore factors that although are not perceived as risks in

the traditional sense, yet are priced by the market. An interesting paper by Ziering and McIntosh

(1999) investigates the relationship between property size and risk-return profile. The paper

analyzes the performance of 4 property size classes within the NCREIF property universe -


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below $20 million, $20 million-$40 million, $40million-$100 million, and over $100 million -

across the 1981-1998 period and within the 4 imbedded phases of the real estate cycle. The

results indicated that property size is a powerful moderator of risk/return across the spectrum of

size, and that the largest category of property, while providing investors with the highest average

return, also exhibits the greatest volatility. The study also showed that there is a significant

difference in the price of risk (i.e. return per unit of risk) between these sizes demonstrating

that asset volatilities and covariance are not the sole factors priced by the market.

The Ziering and McIntosh study led to the inclusion of the size factor in the asset pricing model

developed in my thesis.

The other interesting study was done by Hess and Liang (2005). They created portfolios based onthe size-tiered economic geography groups from the NCREIF data set. They grouped the top-35

U.S. metro areas into seven investment clusters based on size, economic structure and

geographical location. Metro areas beyond the top 35 were named opportunistic markets, and

they collectively represent only 5% of institutional real estate investments. The top-nine markets

are called anchor markets; they are the largest US metro areas and are representative of the

investment characteristics of their respective clusters. The 26 markets that are not anchors are

called major markets and belong to one of the seven clusters.

Interestingly, the nine anchor markets account for about two-thirds of NCRIEF investment value

and nearly half of property value held by public REITS. By contrast about 30% of U.S. income.

Employment and population stem from these markets. The 26 major markets host about 30% of

NCREIF and 30% of REIT investment value, and about one-quarter of U.S. income,

employment and population. This demonstrates the over weighted characteristic of the

NCREIF property universe.

The study concludes Analyzing the return characteristics of NCREIF investments by clusters

seems to verify that diversification using this approach can provide portfolio benefits. Relatively

low return correlations between some categories suggest that risk reduction is possible through

diversification. Although the study displayed an attempt to categorize real estate, the differing


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pricing of risk of these categorizes demonstrates that there are other factors attributed to the US

Metros that are being priced by the market.

This large disparity in investment value and the market price of risk between the top nine

anchor markets, the next 26 major markets and the opportunistic markets led me to include the

propertys Tier location as a possible factor priced by the market, in my investigation.


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Methodology & Data

Methodology in Brief

The main objective of this study is to provide some guidance to real estate core fund portfolio

managers by exploring the historical performance of core properties within the NCREIF property

set from the 1984 to 2003 period. The focus of the analysis is on identifying systematic

determinants of long run investment performance. The study is composed of two parts, the first

involves working with the NCREIF property level data to create distinct portfolios and the

second involves testing of various assets pricing models on these portfolios. The models range

from the single factor CAPM to a multi factor Fama and French based model.

Part I

This involves using the property level data of the NCREIF Index to construct portfolios and

historical return indexes based on property size (value), and based on CBSA tier (that is,

upper, middle, and tertiary cities from an institutional investment perspective). These are

factors that may be systematic determinants of long run investment performance. This stage

involved analyzing the data and experimenting with several categorizations for creating the size

and tier portfolios (obviously property type is easy), to arrive at a portfolios that are distinct and

yet have adequate number of properties to be adequately representative.

Part II

This involved the testing of these portfolios with various asset pricing models.

By observing the historic returns of these portfolios alone, no useful insight can be provide

relating to tactical investment decisions as the return can never be viewed separately from risk.

The introduction of risk was done be applying the CAPM on these portfolios. Market 6 Betas for

6 The Market is defined as the NCREIF aggregate property set.


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these portfolios were calculated using a time series regression and a cross sectional regression

was run using these Market Betas to determine the accuracy of the model.

By charting the Market Betas as representative of risk with the historic returns for these

portfolios and creating clouds around portfolios with similar factors (i.e. a tier cloud, size

cloud and property type cloud) and observing their dispersion I could identify if these factors

where systematically priced by the market.

Although the single factor CAPM does provide some useful insights the search for a more

accurate model led to the development of several other equilibrium asset pricing models The

introduction of the size factor, the tier factor, the income factor and the property type factor,

resulted in a significant model with a high R square that accurately models the market pricing of commercial institutional quality real estate assets.

This is a potentially useful tool for investment managers in making tactical ex ante investment

decisions as well gauging ex-post investment manager performance.

The detailed methodology for each step has been described below.

Detailed Methodology Part I Data Analysis

The NCREIF Database

The NCREIF 7 database contributed the underlying data used for this study. The National Council

of Real Estate Investment Fiduciaries (NCREIF) is an association of institutional real estate

professionals who amongst other activities, collect and process detailed property level data

provided by the data contributing members. The data contributing members comprise of

investment managers and plan sponsors who own or manage real estate in a fiduciary setting.

They represent institutions and corporations ranging from pension funds to asset management

companies. Thus the dataset represents institutional quality commercial real estate. The dataset

7 For further information on NCREIF ref: www.ncreif.com


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began in 1978 with 233 properties totaling a value of $580 million and has expanded rapidly to

4756 properties with a value of $201 billion in 2006 Q1.

NCREIF also produces the NCREIF Property Index (NPI), a quarterly index that shows real

estate performance returns using the data submitted by the Data Contributing Members. The NPI

is used as an industry benchmark to compare an investor's own returns against the industry

average

The income, capital and total returns for my study were calculated directly from the property

level data using the formula used by NCREIF. They are described below:

Income Return

Net Operating Income

Beginning Market Value + 1/2 Capital Improvements - 1/2 Partial Sales - 1/3 NOI

Capital Value Return

(Ending Market Value - Beginning Market Value) + Partial Sales - Capital Improvements

Beginning Market Value + 1/2 Capital Improvements - 1/2 Partial Sales - 1/3 NOI

Total Return

Income Return + Capital Value Return


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Selecting Core Properties

This study is focused on core investments i.e. stabilized properties without excessive capital

expenditures and does not included any opportunistic development or repositioning of these

assets. For this reason I have made a somewhat arbitrary distinction of eliminating the data of

any property in the quarter for which its capital expenditure (Capex) is greater than 20% of its

market value entering into the quarter (Beginning Market Value). Although 20% itself may seem

a high number I have attempted to create a balance as it is true that even core properties

occasionally require a significant capital expenditure for major renovations, in order to maintain

their cash flow.

Selecting the Time Period

The study focused on the performance of properties from 1984 Q1 to 2003 Q4, thus providing

me with 20 years of data and 80 data points for a quarterly analysis. The 1984-2003 period was

selected as it represented a complete real estate cycle. Additionally, the lower number of

properties and suspect accuracy of data in the pre 1984 period as well as the recent run up in real

estate prices post 2003, may have introduced inaccuracies in the study.

Creating the Portfolios

The portfolios were created from the NCREIF database using the Microsoft Access program.

There were a total of 38 portfolios created from the database. There were 18 portfolios each for

the Size and Tier factor resulting from the six property types being further categorized into three

classes each for Size and Tier. Additionally there were two portfolios created from all property

types representing high and low income returns.


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The Property Type Selection

The four main 8 property types were selected with two property types being represented by two

further classifications. The property types classifications are Apartments, Retail, Office located

in Central Business Districts (CBD), Office located in the Suburban areas, Industrial Warehouse,

and Industrial R&D + Flex.

The Retail classification includes all institutional quality retail excluding Regional and Super

Regional Malls. This exclusion was deemed necessary as Regional and Super Regional Malls are

normally not held in core real estate funds and are mostly held by focused Mall REITS as such

properties require specialized management and consolidated holdings to perform competitively.

Apartments were analyzed as one property type. Although further classification into high rise

and garden style would have been beneficial, this classification is fairly recent in the NCREIF

database and thus would not provide sufficient data dating back to 1984.

Office was divided into Office CBD and Office Suburban as their performance is viewed to be

systematically different.

Similarly Industrial was further analyzed as Warehouse and R&D + Flex. Manufacturing was

excluded as Manufacturing properties are normally not part of the core real estate fund portfolio.

Flex was consolidated with R&D as they perform similarly.

Although further classification of property types would be beneficial and allow for a more

detailed analysis I had to balance the accuracy of the research with the number of property types.

The increased classification will result in fewer properties in each portfolio especially in the

early part of the database. This could result in the idiosyncratic returns of a property significantly

affecting the return of the entire portfolio.

8 Hotel was not examined in this study due to the lack of a significant number of properties in the NCREIF dataset.


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The Size Selection

The size portfolios were created based on the market value of the properties and creating high

and low cutoffs. The distribution of the value of properties was considered normal about the

average value. The Low Cut was 0.58 * Average Market Value and the High Cut was 1.42 *

Average Market Value. This was done in order to have an equal number of properties in each

class. This High Cut and Low Cut values were updated every year to reflect the change in capital

value over the years. A total of six categories i.e. Apartments, Office Suburban, Office CBD,

Warehouse, Flex and R&D, Retail (excluding regional and super regional malls), were created.

An example of the creation of the Apartments size classification is shown below:

For Apartments

Average Market Value (year t) = Average of (Ending Market Value + Partial Sales) in year t.

High Cut Year t = Average Market Value (year t) * 1.42

Low Cut Year t = Average Market Value (year t) * 0.58

Small Apartments portfolio in year t: All apartments that have an Ending Market Value plus

Partial Sales less than the Low Cut year t value.

Medium Apartments portfolio in year t: All apartments that have an Ending Market Value plus

Partial Sales between the Low Cut value and High Cut value in year t.

Large Apartments portfolio in year t: All Apartments that have an Ending Market Value plus

Partial Sales above the High Cut year t value.


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The observed final distribution was found to have a larger number of properties falling in the

Medium Size category. However there are sufficient a number of properties across the time

series in each Size category to ensure an accurate representation.

Interestingly the distribution was differently skewed for each property type although I did ensure

that each type was suitably represented.

The performance of the Size portfolios has been provided in a chart form (refer Figure 1 to 18)

and the data has been provided in a numeric form in the Appendix (refer Appendix Table 12 to

17).

Charts Size Portfolios by Property Type

Capital Return Index - Apartments By Size

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

Q u a r t e r l y

I n d e x

L e v e

l

SmallMediumLargeTotal

Figure 1


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Total Return Index - Apartments By Size

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l


Figure 2

Annual Income Return - Apartments By Size

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u

a l I n c o m e R e t u r n ( %


Figure 3


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Capital Return Index - R&D + Flex - By Size

0.0

50.0

100.0

150.0

200.0

250.0

300.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l


Figure 4

Total Return Index - R&D + Flex - By Size

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

900.0

1000.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l

SmallMediumLarge

Total

Figure 5


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Annual Income Return - R&D + Flex By Size

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u a

l I n c o m e

R e

t u r n

( %


Figure 6

Capital Return Index - Warehouse By Size

50.0

70.0

90.0

110.0

130.0

150.0

170.0

190.0

210.0

230.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l

SmallMediumLarge

Total

Figure 7


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Total Return Index - Warehouse By Size

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l


Figure 8

Annual Income Return - Warehouse By Size

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u a

l I n c o m e

R e

t u r n

( %

SmallMediumLarge

Total

Figure 9


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24

Capital Return Index - Office CBD - By Size

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

200.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l


Figure 10

Total Return Index - Office CBD - By Size

0.0

100.0

200.0

300.0

400.0

500.0

600.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l

SmallMediumLarge

Total

Figure 11


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25

Annual Income Return - Office CBD - By Size

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u a

l I n c o m e

R e

t u r n

( %


Figure 12

Capital Return Index - Office Suburban - By Size

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l

SmallMediumLarge

Total

Figure 13


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26

Total Return Index - Office Suburban By Size

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l


Figure 14

Annual Income Return - Office Suburban By Size

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u a

l I n c o m e

R e

t u r n

( %

SmallMediumLarge

Total

Figure 15


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27

Capital Return Index - Retail - By Size

50.0

70.0

90.0

110.0

130.0

150.0

170.0

190.0

210.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l


Figure 16

Total Return Index - Retail - By Size

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r t e r l y

I n d e x

L e v e

l

SmallMediumLarge

Total

Figure 17


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28

Annual Income Return - Retail - By Size

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u a

l I n c o m e

R e

t u r n

( %


Figure 18

The Tier Selection

The Tier portfolios were created based on the total investment value of the NCREIF index in a

particular CBSA. The term "Core Based Statistical Area" (CBSA) as defined by the US Census

Bureau became effective in 2000 and refers collectively to metropolitan and micropolitan

statistical areas. This study is based upon the CBSA 9 classification for each property in 2003 Q4.

Certain CBSAs have been consolidated to represent the primary CBSA (refer Appendix Table 5).

For example Cambridge, Essex County, Rockingham County are combined with Boston and

represented by the Boston CBSA in this study.

All the CBSAs were ranked in order of the total NCREIF investment value in the particular property type. The rank distribution into Tiers was required to optimize several considerations

such as reflecting large jumps in total investment value, represent NCREIF concentrations and

9 For further details on CBSA classification refer www.census.gov


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29

ensure sufficient properties in all Tiers (especially Tier III) that would provide an accurate

representation of returns during the entire analysis period.

The somewhat arbitrary methodology applied to the grouping was to include all ranks in Tier I

until the cumulative number of properties in those ranks was around half 10 the total number of

properties of that property type in the NCREIF database. Tier II included the next ranking

CBSAs until the cumulative number of properties (in Tier II) represented approximately half

those remaining (one quarter of the total). The remaining ranks were classified as Tier III

CBSAs. This grouping was adjusted one or two positions up or down depending if there was a

substantial fall in total investment value in any CBSA near the break point as this represented a

clearer Tier break point.

The rankings were calculated in 2003 Q4 and fixed for the entire historic period. This prevented

CBSAs from moving Tiers and reflected the investment in a Tier over the entire time horizon.

As the rankings would differ by property type, each property type was analyzed separately and

ranked in 2003 Q4. As in the Size category described earlier, a total of six categories i.e.

Apartments, Office Suburban, Office CBD, Warehouse, Flex and R&D, Retail (excluding

regional and super regional malls), were created.

Due to the limitation of the MS Access query function, for a CBSA to be included in the analysis

there has to be at least one property in that CBSA in 2003 Q4. That is, if there is a property that

has been transacted in a particular CBSA before 2003 Q4 that does not have even one property in

2003 Q4 then that CBSA will not be part of the analysis and the performance of that property

will not be reflected in the Tiers. This would in some way skew the data in Tier III as some

CBSAs in Tier III will not be part of the analysis. However this has proved to occur rarely and

has not influenced the performance of the Tiers significantly.

An example of the Retail property type distribution has been provided below:

10 This represented the over-weighting


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Retail

Tier No. of Properties MSA RankingsI 231 1 to 12

II 123 13 to 35III 108 36 to 107Total 462 properties 107 MSAs

The detailed Tier break up for each property type as well as the CBSA listing for each of these

Tiers has been provided in the Appendix (refer Appendix Table 6 to 11).

The performance of the Tier portfolios has been provided in a chart form (refer Figures 19 to 36)

and the data has been provided in a numeric form in the Appendix (refer Appendix Table 18 to

23).

Charts Tier Portfolios by Property Type

Capital Return Index - Apartments By Tier

50.0

70.0

90.0

110.0

130.0

150.0

170.0

190.0

210.0

230.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r

t e r l y

I n d e x

L e v e l

Tier ITier IITier IIITotal

Figure 19


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31

Total Return Index - Apartments By Tier

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

900.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u a r

t e r l y

I n d e x

L e v e l


Figure 20

Annual Income Return - Apartments By Tier

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u



Figure 21


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32

Capital Return Index - Warehouse By Tier

50.0

70.0

90.0

110.0

130.0

150.0

170.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 22

Total Return Index - Warehouse By Tier

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 23


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33

Annual Income Return - Warehouse By Tier

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u



Figure 24

Capital Return Index - Office CBD - By Tier

50.0

70.0

90.0

110.0

130.0

150.0

170.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 25


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34

Total Return Index - Office CBD - By Tier

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 26

Annual Income Return - Office CBD - By Tier

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u



Figure 27


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35

Capital Return Index - Office Suburban By Tier

50.0

60.0

70.0

80.0

90.0

100.0

110.0

120.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 28

Total Return Index - Office Suburban By Tier

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 29


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36

Annual Income Return - Office Suburban By Tier

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u



Figure 30

Capital Return Index - R&D + Flex - By Tier

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 31


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37

Total Return Index - R&D + Flex By Tier

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 32

Annual Income Return - R&D + Flex - By Tier

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u



Figure 33


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38

Capital Return Index - Retail By Tier

50.0

70.0

90.0

110.0

130.0

150.0

170.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 34

Total Return Index - Retail By Tier

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Years

Q u

a r t e r l y

I n d e x

L e v

e l


Figure 35


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39

Annual Income Return - Retail By Tier

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Years

A n n u



Figure 36

Detailed Methodology Part II Asset Pricing Models

As we observed earlier the returns of the portfolios created in Part I have limited use to a

portfolio investment manager without a measure of risk associated with these portfolios. In this

part I will describe the methodology used to create various equilibrium asset pricing models that

I have developed to understand the risks and factors that the market recognizes to price real

estate.

The Single Factor Capital Asset Pricing Model

This involved running several regressions in a two stage process as follows:

1. Time Series Regression: This regression was run for all portfolios to estimate the Beta of the

portfolio relative to the aggregate of all NCREIF properties.


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The U.S. 30 Day Government Treasury Bill total return was used as a proxy for the risk free rate

used to calculate the risk premiums in this study.

The beta for the portfolios was defined with respect to the performance of the aggregate of all

NCREIF properties rather than with respect to the National Wealth Portfolio (NWP). This

simplification avoids appraisal bias, and is consistent with classical CAPM theory under the

assumption that the national wealth-based betas of property portfolios equals their betas with

respect to NCREIF times the beta of the aggregate NCREIF portfolio with respect to national

wealth.

Regression:

R i,t R f,t = i,t + i,t (R m,t R f,t) + i,t

Where:

Ri,t is the Total Return of the portfolio at time t.

Rf,t is the Risk Free Rate at time t.

Rm,t is the Total Return of the aggregate of NCREIF properties at time t.

2. Cross Sectional Regression: This regression was run using the i estimates from the first stage

regression along with their respective average risk premiums [Avg(Ri-Rf)].

Regression:

Avg(R i-R f ) = 0 + 1 i + i

Where:

Ri is the average Total Return of the portfolio.


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Rf is the average Risk Free Rate

i is the Beta of the portfolio estimated from the earlier time series regression.

The cross sectional regressions where run separately over the Tier set of portfolios and the Size

set of portfolios with 18 data points each. This was done to prevent duplication of properties in

the cross sectional regressions. Thus I got two separate cross sectional regression results.

The Multi Factor Equilibrium Asset Pricing Model

Similar to the single factor model this involved running a series of regressions in a two stage

process. However these regressions involved additional factors as described below:

The Size Factor : This represented the size (value) effect and was calculated as total return on

large properties minus the total return on small properties. This factor was derived from the

portfolios already created as below:

R LMS,t = 1/6(R Apt L,t + R Ret L,t + R CBD L,t + R Sub L,t + R Whr L,t + R R&D L,t ) 1/6(R Apt S,t + R Ret S,t + R CBD

S,t + R Sub S,t + R Whr S,t + R R&D S,t )

The Tier Factor : This represented the Tier effect and was calculated as total return on Tier I

properties minus total return on Tier III properties. This factor was also derived from the already

created portfolios as below:

R IMIII,t = 1/6(R Apt I,t + R Ret I,t + R CBD I,t + R Sub I,t + R Whr I,t + R R&D I,t ) 1/6(R Apt III,t + R Ret III,t + R CBD

III,t + R Sub III,t + R Whr III,t + R R&D III,t )

The Income Factor : This represented the income effect and introduced the possible market

preference for a high income component of total return. This factor was created by generating

separate high income and low income portfolios and calculated as total return of low income

return properties minus total return of high income return properties.


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R LMH,t = R L,t R H,t

Although I did run this four factor model, the Income Factor proved to be insignificant and thus I

have only described the three factor model which excluded the Income Factor.

1. Time Series Regression: This regression was run for all portfolios to estimate the Beta of the

portfolio relative to the aggregate of all NCREIF properties as well as to estimate the Factor

Betas.

Regression:

R i,t R f,t = i,t + Mi,t (R m,t R f,t) + IMIIIi,t (R IMIII,t ) + LMSi,t (R LMS,t ) + i,t

Where:

Ri,t is the Total Return of the portfolio at time t.

Rf,t is the Risk Free Rate at time t.

Rm,t is the Total Return of the aggregate of NCREIF properties at time t.

R IMIII,t is the Total Return of Tier I properties at time t minus Total Return of Tier III

properties at time t.

R LMS,t is the Total Return of Large properties at time t minus Total Return of Small

properties at time t.

2. Cross Sectional Regression: This regression was run using the Mi,t , IMIIIi,t , LMSi,t estimates

from the first stage regression, dummy variables for property type along with their respective

average risk premiums [Avg(Ri-Rf)]

Regression:

Avg(R i-R f ) = 0 + 1 Mi + 2 IMIIIi + 3 LMSi + 4 Apt i + 5 Sub i + 6 Whr i + 7 R&D i + 8 Ret i +

i


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43

Where:

Ri is the average Total Return of the portfolio.

Rf is the average Risk Free Rate

Mi is the Market Beta of the portfolio estimated from the earlier time series regression.

IMIIIi is the Tier Beta of the portfolio estimated from the earlier regression.

LMSi is the Size Beta of the portfolio estimated from the earlier regression.

Apt i is 1 if the portfolio represents Apartments 0 otherwise.

Sub i is 1 if the portfolio represents Suburban Office properties 0 otherwise.

Whr i is 1 if the portfolio represents Industrial Warehouse 0 otherwise.

R&D i is 1 if the portfolio represents R&D plus Flex properties 0 otherwise. Ret i is 1 if the portfolio represents Retail properties 0 otherwise.

As property types are dummy variables, Office CBD will represent the base case.

Sample regression line

Dependent Independent

Ri sk Pre mium Bet aNcrei f Bet aTier BetaSi ze Apt Sub Whr R&D RetCBD I 2.75% 1.57 0.31 1.09 0 0 0 0 0

As in the single factor model the cross sectional regressions where run separately over the Tier

set of portfolios and the Size set of portfolios with 18 data points each.


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Analysis & Findings

I tested several equilibrium asset pricing models and have presented in detail the two models that

prove to be most relevant and/or significant. All the models tested have been briefly described below:

1. Single Factor CAPM: This has been described in detail in Chapter 2.

2. Three Factor Model: The three factors, were the Market 11, Size and Tier factors. This

model had significant coefficients for all the factors, but proved to have a low adjusted R

square.

3. Three Factor Model with Property Type Dummies: This has been described on detail in

Chapter 2. This introduced the property type as a factor in the initial three factor model.

All the factors proved to be significant except for the Market factor. This model also had

the highest adjusted R square and is the model selected by this paper. I have described the

findings of this model in the later part of this chapter.

4. Four Factor Model: This included the income factor described earlier as the fourth factor.

However the income factor proved to be insignificant, the model had a reduced adjusted

R square and was subsequently rejected.

5. Four Factor Model with Property Type Dummies: This model introduced the property

type dummies in the four factor model described above. The income factor remained

insignificant and the adjusted R square although high, was less then the similar three

factor model (Model 3). This model was subsequently rejected as it presented no new

information and/or accuracy.

The findings of the single factor model and the three factor model proved to be very interesting. I

have described the findings for these two models in detail below:

11 Market refers to the NCREIF collection of properties


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The Single Factor Capital Asset Pricing Model

A) The results of the time series regression proved to be very interesting. I have plotted the

results of the portfolio Market Beta with the average return of that portfolio to get an early image

of the risk / return profile of the portfolios. I have also created clouds around the portfolios

representing the factors. This was done to check if the factors tend to aggregate in a particular

area of the risk / return spectrum (i.e. does the market systematically price these factors?)

The charts have been presented below (Figures 37 to 40)

Property Type Tier Analysis - Risk (Beta) Vs Return

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Beta (NCREIF)

T o

t a l R e

t u r n

%

Apts

Ret

Whr

CBD

R&D

Sub

Figure 37


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46

Property Type Size Analysis - Risk (Beta) vs Return

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

Beta (NCREIF)

T o

t a l R e

t u r n

%

Apts

Ret

Whr

R&D

CBD

Sub

Figure 38

Size Analysis- Risk (Beta) vs Return

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

Beta (NCREIF)

T o

t a l R e

t u r n

%

Large

Medium

Small

Figure 39


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47

Tier Analysis- Risk (Beta) Vs Return

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Beta (NCREIF)

T o

t a l R e

t u r n

%

Tier II

Tier III

Tier I

Figure 40

The first interesting finding is that the portfolios with a higher Market Beta have lower historic

total returns (which are a proxy for expected returns). This seems counter intuitive to the CAPM

theory.

The other interesting finding is the clear aggregation of the portfolios by property type (refer

Figure 37 & 38), implying that this factor is systematically priced by the market. This was later

confirmed in the multi factor model described earlier.

The Size factor also presented some aggregation (refer Figure 39) although less distinct as that of the property type factor. From the aggregation it seems that the market requires a premium for

investing in larger value properties and a discount for investing in smaller value properties.

The Tier factor did not have a clear aggregation (refer Figure 40).


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48

B) As described earlier the model consisted of running the cross sectional regression twice i.e.

over the Size and Tier portfolios, so as to avoid duplication of portfolios. Both the regression

results have been presented below (Tables 1 & 2).

Regression Analysis CAPM Cross Sectional - Tier Analysis

r 0.679 n 18r -0.824 k 1

Std. Error 0.012 Dep. Var. Risk Premium

ANOVA tableSource SS df MS F p-value

Regression 0.0046 1 0.0046 33.92 2.59E-05Residual 0.0022 16 0.0001

Total 0.0067 17

Regression output confidence interval variables coefficients std. error t (df=16) p-value 95% lower 95% upper Intercept 0.0712 0.0081 8.817 1.54E-07 0.0541 0.0883

CoBeta -0.0420 0.0072 -5.824 2.59E-05 -0.0573 -0.0267

Table 1


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Regression Analysis CAPM Cross Sectional - Size Analysis

r 0.438 n 18r -0.662 k 1

Std. Error 0.019 Dep. Var. Y

ANOVA tableSource SS df MS F p-value Regression 0.0044 1 0.0044 12.46 .0028

Residual 0.0057 16 0.0004Total 0.0101 17

Regression output confidence interval variables coefficients std. error t (df=16) p-value 95% lower 95% upper Intercept 0.0784 0.0139 5.625 3.80E-05 0.0488 0.1079

CoBeta -0.0443 0.0125 -3.530 .0028 -0.0709 -0.0177

Table 2

CAPM Cross Regression - Tier Analysis

-8.00%

-7.00%

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%-2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00%

Historic Risk premium

P r e

d i c t e d R i s k P r e m

i u m

Figure 41


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50

As can be seen from the above regression results (refer Table 1 & 2), the single factor CAPM

model does not prove to be a robust model for pricing risk in real estate investments. It has a

significant intercept and a low R square and actually provides a negative Beta to the market

implying that the market requires a lower risk premium for portfolios with a higher Market Beta

as compared to portfolios with a lower Market Beta. This does not make intuitive sense and leads

into my second risk model in which I try and capture other factors that the market prices as if

they were risk.

Three Factor Fama & French Based Asset Pricing Model with Property Type

This model proved to be a very robust asset pricing model with a high R square and a near zero

and insignificant intercept.

Regression Analysis 3 Factor FF + Dummy - Tier

R 0.951 Adjusted R 0.908 n 18

R 0.975 k 8Std. Error 0.006 Dep. Var. Risk Premium


Regress ion 0.0064 8 0.0008 21.85 . 0001Residual 0.0003 9 0.0000

Total 0.0067 17

Regression output confidence interval var iables coefficients s td. er ror t (df=9) p-value 95% lower 95% upper Intercept 0.0028 0.0229 0.121 .9066 -0.0491 0.0547

CoBetaNcreif -0.0041 0.0156 -0.263 .7981 -0.0395 0.0312CoBetaTier 0.0073 0.0029 2.538 .0318 0.0008 0.0139CoBetaSize 0.0179 0.0047 3.817 .0041 0.0073 0.0285

BetaApt 0.0486 0.0138 3.525 .0065 0.0174 0.0798BetaSub 0.0092 0.0057 1.615 .1408 -0.0037 0.0221BetaWhr 0.0344 0.0114 3.012 .0147 0.0086 0.0603BetaR&D 0.0306 0.0061 5.000 .0007 0.0168 0.0445

BetaRet 0.0405 0.0128 3.164 .0115 0.0116 0.0695

Table 3


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51

Regression Analysis 3 Factor FF + Dummy - Size

R 0.967 Adjusted R 0.938 n 18

R 0.983 k 8Std. Error 0.006 Dep. Var. Y


Regression 0.0098 8 0.0012 33.07 8.75E-06Residual 0.0003 9 0.0000

Total 0.0101 17

Regression output confidence interval var iables coefficients s td. er ror t (df=9) p-value 95% lower 95% upper Intercept 0.0292 0.0170 1.720 .1196 -0.0092 0.0677

CoBetaNcreif -0.0294 0.0109 -2.697 .0245 -0.0541 -0.0047CoBetaTier 0.0204 0.0046 4.424 .0017 0.0099 0.0308CoBetaSize 0.0420 0.0033 12.556 5.23E-07 0.0344 0.0495

BetaApt 0.0463 0.0112 4.134 .0025 0.0210 0.0716BetaSub 0.0249 0.0057 4.414 .0017 0.0122 0.0377BetaWhr 0.0248 0.0087 2.860 .0188 0.0052 0.0444BetaR&D 0.0337 0.0054 6.252 .0001 0.0215 0.0459

BetaRet 0.0342 0.0102 3.354 .0085 0.0111 0.0573

Table 4

Three Factor Fama French + Property Type - Tier Portfolios

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

-2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00%

Historic Returns

P r e

d i c t e d R e

t u r n s

Figure 42


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Three Factor Fama French + Property Type - Size Portfolios

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

-3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00%

Historic Return

P r e

d i c t e d R e

t u r n

Figure 43

The above model proves to be an accurate asset pricing model (refer Table 3 & 4). It is

interesting to observe the coefficients of the factors as they seem often opposite to the Fama &

French model within the stock market. An important point to note is that this analysis only

includes total returns on the property level. At a fund level there may be additional costs such as

transaction, operating or management costs that may differ (at the fund level) by property type,

size or tier. However on further discussion with fund managers 12, these additional costs were

considered insignificant.

The Market factor , the beta with respect to the aggregate NCREIF is found to be insignificant

and possibly negative influence on expected return. This is the opposite of what asset pricingtheory predicts. It is difficult to ascertain what the possible reasons for this may be. One possible

reason could be that the market beta for the portfolios does not stay constant over time and

changes randomly and thus it cannot be systematically predicted. As a result it is not priced by

12 Cate Polleys, John Barry, Real Estate Fidelity Asset Management


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the market. This could be ascertained by doing the analysis over several shorter periods and

observing if the betas change significantly over the different periods. However as any

meaningful analysis will have to include an entire real estate cycle, the NCREIF database does

not provide sufficient historic data to test this hypothesis.

The Size factor , works opposite to the way it does in the stock market 13, with larger properties

commanding an expected return premium. This could possibly signify a illiquidity premium as

it may be more difficult to sell larger properties then smaller properties in a market downturn.

This hypothesis could be further analyzed by creating a illiquidity factor that represents

transactions (in terms of numbers transacted / total properties as well as shelf time) for the

portfolios over the historic period.

The Tier factor , surprisingly gives an expected return premium to properties in upper tier

CBSAs. However the coefficient value is small as compared to that of the other factors

signifying that this factor has limited influence. This premium seems counter intuitive to a

possible illiquidity factor as it is seems that selling properties in Tier III CBSAs will prove to

be more difficult due to the lack of a deep market for institutional quality commercial real

estate.

The Property Type facto r, proved to be the most significant determinant (collectively) of market

pricing, with decreasing risk premiums required in the order of Apartments, Retail, R&D,

Warehouse, Suburban Office and CBD Office. Again it is difficult to ascertain the reasons for

this pricing. This could represent a systematic personal preference of the investment managers,

stemming from their varying comfort levels with particular property types (for example

managers may be more comfortable assessing risks associated with the longer term brand name

tenants in office properties rather than those with the shorter term, numerous unknown tenants in

apartments). This could also represent the risk averse nature (on a personal level) of the

investment manager. He / she would prefer to hold larger flashy office properties as they visually

appear to be solid investments to the investor (picture on the wall affect).

13 Small cap stocks typically command a risk premium over large cap stocks possibly signifying a illiquidity premium required as small cap stocks trade less frequently and have a higher bid-ask spread.


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Summary & Conclusions

This thesis finds that an equilibrium asset pricing model consisting of the two Fama-French-like

factors, property size and MSA tier, plus property type dummy variables, explains some 90% of the long-run historical cross-section of core property portfolio returns. Interestingly (and in

contrast to the stock market), the market factor, the beta with respect to aggregate NCREIF, is

found to be insignificant, and possibly a negative influence on expected return. (We still leave it

in the model for the sake of form.) Furthermore, the size factor works opposite to the way it does

in the stock market, with larger properties commanding an expected return premium.

Surprisingly, the city tier factor gives a price discount (expected return premium) to upper tier

cities. The main determinant was the property type factor. Tests for an income factor (similar

to the Fama-French book-to-market factor) found this factor to be insignificant. Thus, the

equilibrium asset price model that seems to work well within the institutional core real estate

asset class seems to be very different from, almost opposite to, the analogous model within the

stock market.

The direct application of this study by a portfolio manager depends on his/her philosophical view

of this study. If the manager is confident in the accuracy of his/her pricing preferences and these

preferences are different from those of the market (i.e. that apartments should not command a

premium, and/or that large properties shouldnt require a premium) then this model clearly

shows the premiums for each of the factors and thus the opportunity for superior risk adjusted

returns based on the managers preferences.

If the manager believes that his/her pricing preferences should be consistent with those of the

markets (market knows best) then this model can be used to evaluate investment decisions ex

ante. If a projected investment can produce superior returns based on the mangers own projections (higher than the market equilibrium return projected by the model), then this is a

projected positive alpha 14 generating investment and one should proceed with the investment.

This model can then also be used to test the ex-post performance of a portfolio manager by

14 Higher returns with no additional risk)


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adjusting his/her portfolio for the model factor premiums and testing if the manger produced

alpha.

However it is important to understand the limitation of this model before making investment

decisions. This model is an accurate asset pricing model of the historic NCREIF database. If one

believes that recently commercial real estate has undergone a systematic 15 change in pricing then

the factor coefficients may have changed significantly and the model will not accurately reflect

the market asset pricing going forward .

15 This is the view of some investment managers that I have spoken with


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Study Limitations and Scope for Further Research

Limitations

The study is limited by the relatively short time span of the NCREIF database. The data begins in

1978 as compared to data from the stock market which begins from 1925 (CRSP monthly data).

As such I have only been able to include one real estate cycle for this analysis. Ideally the study

should have included several cycles as well as analyzed each cycle separately to identify if the

factor coefficients change significantly over time 16.

The study is also limited by the accuracy of the NCREIF database. The beginning entries of the

database may have less accuracy than later. This issue has been some what circumvented by

beginning my analysis from 1984, a period by which the database had considerably improved.

Another possible limitation is the limited number of properties in each portfolio, mainly in the

earlier period. In 1984 the total number of properties in the NCREIF database was 994 and in

2003 it was 4,055. All possible care was to taken to ensure adequate number of properties in

each portfolio in the early period. As the variations in the returns for the properties within a

portfolio are idiosyncratic, there will be a wider range in the estimation of the beta.

Scope for further research

The study has shown that the Size, Tier and Property Type factors are significant and the high R

square of the multi factor model demonstrates that almost all factors that the market prices have

been included in this model. Interestingly, it is difficult to interpret how and why the market

prices these factors. These factors are likely proxies for quantitative risks such as illiquidity or fund level expenses, or they could be proxies for qualitative systematic behavioral preferences of

the investment managers. Some of the possible proxies have been described in Chapter 4. Further

16 Stock betas are calculated over a period of five years the time period during which they remain mostly the same.


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research can confirm these proxies if, by adding representative factors in the model, the existing

factors loose significance.

It is important to note that the reasons mentioned for the factor pricing described earlier are of

the personal view of the author and have not been quantitatively researched. This is one of the

areas that have the potential for further research.

This study has been conducted with the assumption that the beta of the portfolio with respect to

the National Wealth Portfolio (NWP) is equal to the beta of the portfolio with respect to the

NCREIF aggregated portfolio times the beta of the NCREIF portfolio with respect to the NWP.

This assumption has proved to be accurate in earlier studies but may be tested by conducting this

research directly with respect to the NWP. However this would involve the un smoothening 17of the NCREIF data in order to make an apples to apples comparison.

As described earlier the NCREIF data set is weighted towards large size commercial real estate

located in Tier I CBSAs. Thus the exposure of this research to small value properties in Tier III

CBSAs is limited. Possible further research would involve completing a similar study based on

a more comprehensive database such as that of Portfolio Property Research (PPR). However

although these databases cover a wider spectrum of properties the time period of the database is

limited. In any case covering the recent five years would provide an interesting comparison.

17 This is due to the appraisal based valuation of the NCREIF database. Un smoothening can be done by anautoregressive process Refer Geltner and Miller (2001)


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Bibliography

Black, F. Beta and Return. Journal of Portfolio Management 20: 8-18, fall 1993.

Black, F., M. Jensen, and M. Scholes. The Capital Asset Pricing Model: Some EmpiricalTests. In M. Jensen (ed.), Studies in the Theory of Capital Markets , Praeger Inc., New York,

NY. 1972.

Bodie, Z., A. Kane and A.J. Marcus. Investments , 5 th ed., McGraw-Hill, New York, NY. 2002.

Brealey, R.A. and S.C. Myers. Principles of Corporate Finance , 7 th ed., McGraw-Hill, NewYork, NY. 2003.

Fama, E. and K. French. The Cross-Section of Expected Stock Returns. Journal of Finance47(2): 427-465, June 1992.

Fama, E. and J. MacBeth. Risk, Return, and Equilibrium: Empirical Tests. Journal of Political Economy 81: 607-636, May 1973.

Geltner, D. Estimating Real Estates Systematic Risk from Aggregate Level Appraisal-BasedReturns. AREUEA Journal 17(4): 463-481, winter 1989.

Geltner, D. Smoothing in Appraisal-Based Returns. Journal of Real Estate Finance & Economics 4(3): 327-345, September 1991.

Geltner, D. and N.G. Miller. Commercial Real Estate Analysis and Investments , 1st ed., South-Western/College Publishing Co., Mason, OH. 2001.

Ling, D. and A. Naranjo. Economic Risk Factors and Commercial Real Estate Returns. Journal of Real Estate Finance & Economics 14(3): 283-307, May 1997.

Ling, D. and A. Naranjo, The Fundamental Determinants of Commercial Real Estate Returns. Real Estate Finance 14(4):13-24, Winter 1998.

Ling, D. and A. Naranjo, The Integration of commercial Real Estate Markets and Stock Markets. Real Estate Economics 27(3): 483-516, fall 1999.

Lintner, J. The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Captial Budgets. Review of Economics and Statistics 47:13-37, February 1965.

Markowitz, H. Portfolio Selection. Journal of Finance 7: 77-91, March 1952.Mei, J. and A. Lee. Is There a Real Estate Factor Premium. Journal of Real Estate Finance &

Economics 9(2): 113-126, September 1994.

National Council of Real Estate Investment Fiduciaries website,


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indices/npi.phtml?type=national>, accessed June 2006.

Sharpe, W. Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. Journal of Finance 19: 425-442, September 1964.

Hess, R and Liang, Y. Size-Tiered Economic Geography: An Update Pramerica Real Estate Investors , December 2005 www.pramerciarei.com

Ziering, B and McIntosh, W. Property size and risk: Why bigger is not always better Journalof Real Estate Portfolio Management Boston:1999 Vol. 5, Iss. 2, p.105-112

Li, N and Price, S.M. Multiple Assets Class Investing: Equilibrium Asset Pricing Evaluations of Real Estate Risk and Return across Four Quadrants MSRED Thesis, MIT, 2005


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Appendix

Table 5: Details of Combined CBSAsNumber of

records CBSA CBSA Name CBSAorDIV

2236 14460 MA - Boston 144842608 14460 MA - Cambridge 15764

328 14460 MA - Essex County 21604

152 14460NH - RockinghamCounty 40484

14830 16980 IL - Chicago 169741382 16980 IL - Lake County 29404

16 16980 IN - Gary 2384412170 19100 TX - Dallas 19124

2033 19100 TX - Fort Worth 23104636 19820 MI - Detroit 19804

1501 19820 MI - Warren 4764413325 31100 CA - Los Angeles 31084

7118 31100 CA - Santa Ana 420443249 33100 FL - Fort Lauderdale 227442067 33100 FL - Miami 331242236 33100 FL - West Palm Beach 484241756 35620 NJ - Edison 20764

627 35620 NJ - Newark 35084486 35620 NY - Nassau 35004

3515 35620 NY - New York 35644425 37980 DE - Wilmington 48864

1259 37980 NJ - Camden 158042937 37980 PA - Philadelphia 379645425 41860 CA - Oakland 360843561 41860 CA - San Francisco 418846665 42660 WA - Seattle 42644

315 42660 WA - Tacoma 451048897 47900 DC - Washington 478943045 47900 MD - Bethesda 13644


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Table 6: Tier Distribution - Apartments

CBSA Order CBSAName47900 1 DC - Washin gton33100 2 FL - Miami19100 3 TX - Dallas16980 4 IL - Chicago31100 5 CA - Los Angeles

35620 6 NY - New York12060 7 GA - Atlanta4 18 60 8 CA - Sa n F ra nc is co41740 9 CA - San Diego19740 10 CO - D enver 26420 11 TX - H ou ston38060 12 AZ - Phoenix14460 13 MA - Boston42660 14 WA - Se attle12420 15 TX - Austin29820 16 NV - Las Vegas36740 17 FL - Or lando37980 18 PA - Phi lade lphia45300 19 FL - Tampa4 01 40 2 0 CA - R iv er si de3 34 60 2 1 MN - Mi nn ea po li s38900 22 OR - Portland1 67 40 2 3 NC - Ch arl otte

2 81 40 2 5 MO - Ka ns as Ci ty19820 26 MI - D etroit39580 27 NC - Raleigh41620 28 UT - Sal t Lake City4 11 80 2 9 MO - St . L ou is32820 30 TN - Memphis1 48 60 3 1 CT - Br id ge po rt37100 32 CA - Oxnard20500 33 NC - Durham1 07 40 3 4 N M - Al bu que rq ue26900 35 IN - Indianapol is46700 36 CA - Vallejo3 83 00 3 7 PA - Pi tts bu rg h25540 38 CT - H artford17820 39 CO - Colorado Spr ings4 00 60 4 0 VA - R ic hmo nd18140 41 OH - C olu mbus1 71 40 4 2 O H - C inc in nat i3 49 80 4 3 T N - N as hv il le4 17 00 4 4 T X - Sa n An to ni o46060 45 AZ - Tucson46140 46 OK - Tulsa39900 47 NV - Reno2 72 60 4 8 F L - J ac ks on vi ll e41940 49 CA - San Jose1 38 20 5 0 AL - Bi rmi ng ha m45940 51 NJ - Tre nton4 09 00 5 2 CA - Sa cr ame nto1 74 60 5 3 O H - C lev el an d39100 54 NY - Poughkeepsie2 43 40 5 5 MI - G ra nd R ap id s3 93 00 5 6 RI - Pr ov id en ce42140 57 NM - Santa Fe2 80 20 5 8 MI - Kal ama zo o3 17 00 59 N H - Ma nc he ste r 3 33 40 5 9 W I - M il wa uk ee36540 61 NE - Omaha1 79 00 6 2 SC - Co lu mb ia4 22 20 6 3 CA - Sa nta R os a2 48 60 6 4 SC - G re en vi ll e4 93 40 6 5 MA - Wor ce ste r 1 59 80 6 6 F L - C ape C or al2 66 20 6 7 AL - H un ts vi ll e114 60 6 8 MI - An n Ar bo r 2 50 60 6 9 MS - G ul fp or t37340 70 FL - Palm Bay2 99 40 7 1 KS - L awr en ce

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